Yes 고맙다 감사하다 both mean "thanks" the ㅂ니다 form is the most polite one: 고맙습니다 or 감사합니다 the 요 form is standard polite: 고마워요 or 감사해요 without 요 form is informal: 고마워 (감사해 is not really used often) so you'd say 고마워 to a very close (or younger) friend/family member and 감사합니다 with unknown/high people (for example when asking directions on the street or ordering food).

When you want to say thanks to a friend you use 고마워. And when you want to say thank you to an older person or politely you can use 감사합니다.

감사합니다 is polite way of saying. You can say 고마워 to who is younger than you are or same age as you are unless you aren't familiar each other like meeting first time

If you look at those words deeply, they are distinguished from each other. 고맙다, 감사하다 botn can be used for any situation but deep inside, 고맙다 is for someone helps you. 감사하다 is for just thanking someone even someone dosen't help you now. F.Y.I you thanks your father, he is not helping you now but when u think of him. You just thank him for what he already has done before. You are happy and thank him when you just think of him. 감사하다 has that kind of "thank you".